When I attempt to begin a game, I get an error

This forum is for community based troubleshooting of technical issues with the game. There is no one here that can email you to discuss issues. If you need direct Blizzard Support for any issue, you would need to use the support button at the top of this page and choose contact support. That would allow you to submit a web ticket.

That said the issue you experienced is one that is being investigated as a potential bug and as you have already discovered the work around is to restart the game client.

There is no ETA on a permanent solution to this issue but the investigation is ongoing.